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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Open relation theorem without closedness assumptions


Author: Szymon Dolecki
Journal: Proc. Amer. Math. Soc. 109 (1990), 1019-1024
MSC: Primary 90C25; Secondary 46A30, 90C48
DOI: https://doi.org/10.1090/S0002-9939-1990-1012926-2
MathSciNet review: 1012926
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Abstract: It is shown that a convex relation such that the preimage of a bounded set has nonempty interior is lower semicontinuous throughout the algebraic interior of its domain. If, besides, the relation is closed-valued, then it is closed throughout the algebraic interior of its domain.


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DOI: https://doi.org/10.1090/S0002-9939-1990-1012926-2
Article copyright: © Copyright 1990 American Mathematical Society